【摘要】：非線性偏微分方程是一門歷史久遠(yuǎn)的學(xué)科,它是出現(xiàn)在各個(gè)科學(xué)領(lǐng)域中非常重要的數(shù)學(xué)模型.本文利用計(jì)算機(jī)代數(shù)為輔助工具,對(duì)非線性偏微分方程的三個(gè)問題進(jìn)行了研究,它們分別是非局域?qū)ΨQ、相互作用解以及守恒律.本文內(nèi)容主要分為以下五部分:第一章,對(duì)非線性偏微分方程的解和守恒律的若干求法進(jìn)行了簡(jiǎn)要的介紹,并闡明了本文的主要研究?jī)?nèi)容.第二章,詳細(xì)闡述了論文所需要的基本理論知識(shí).第三章,首先介紹了(2+1)-維Kaup-Kupershmidt方程組的背景知識(shí),然后給出了關(guān)于該方程組的非局域?qū)ΨQ和相互作用解.第四章,首先給出了Kadomtsev-Petviashvili勢(shì)方程的相關(guān)研究背景,再運(yùn)用Noether法得到了許多該方程的守恒律.第五章,對(duì)全文提出總結(jié)并作出展望.
[Abstract]:Nonlinear partial differential equation (NPDE) is a long history subject, and it is a very important mathematical model appearing in various fields of science. In this paper, three problems of nonlinear partial differential equations are studied by means of computer algebra. They are nonlocal symmetry, interaction solutions and conservation laws. The content of this paper is divided into the following five parts: the first chapter briefly introduces the solutions of nonlinear partial differential equations and some methods of finding conservation laws, and expounds the main research contents of this paper. The second chapter, elaborated the basic theory knowledge which the thesis needs. In chapter 3, the background knowledge of (21) -dimensional Kaup-Kupershmidt equations is introduced, and then the nonlocal symmetry and interaction solutions of the equations are given. In chapter 4, the research background of the Kadomtsev-Petviashvili potential equation is given, and then many conservation laws of the equation are obtained by using the Noether method. The fifth chapter, the full text proposed the summary and makes the prospect.
【學(xué)位授予單位】：寧波大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175.29

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本文編號(hào)：2370247